12 Questions
What is the definition of a fraction, and what are its two main components?
A fraction is a way to express a part of a whole, and it consists of a numerator (top number) and a denominator (bottom number).
What is the difference between like and unlike fractions?
Like fractions have the same denominator, whereas unlike fractions have different denominators.
How do you add fractions with like denominators?
Add fractions with like denominators by adding the numerators and keeping the same denominator.
What is the simplest form of a fraction, and why is it important?
The simplest form of a fraction is when it has no common factors between the numerator and denominator, and it is important because it makes fractions easier to work with and compare.
How do you compare two fractions to determine which one is greater?
A fraction is greater than another if its numerator is greater or its denominator is smaller.
What is one real-world application of fractions?
Fractions are used to measure lengths, capacities, and weights.
What is the symbol used to represent the proportionality between two quantities, and what does it read as?
The symbol is ∝, and it reads as 'is proportional to'.
If x and y are in direct proportion, what is the equation that represents their relationship?
x = ky
What happens to y when x increases in an inverse proportion relationship?
y decreases
What is an example of a real-world application of inverse proportion?
Time taken to travel a distance
What is the equation that represents the relationship between x and y in inverse proportion?
x = k/y
What happens to x when y becomes infinite in an inverse proportion relationship?
x becomes zero
Study Notes
Fractions
Definition
A fraction is a way to express a part of a whole. It consists of a numerator (top number) and a denominator (bottom number).
Key Concepts
- Equivalent Fractions: Fractions that have the same value, but different numerators and denominators.
- Simplest Form: A fraction in its most basic form, with no common factors between the numerator and denominator.
- Like Fractions: Fractions with the same denominator.
- Unlike Fractions: Fractions with different denominators.
Operations with Fractions
- Addition: Add fractions with like denominators by adding the numerators and keeping the same denominator.
- Subtraction: Subtract fractions with like denominators by subtracting the numerators and keeping the same denominator.
- Multiplication: Multiply fractions by multiplying the numerators and denominators separately.
- Division: Divide fractions by inverting the second fraction (i.e., flipping the numerator and denominator) and then multiplying.
Comparing Fractions
- Greater Than: A fraction is greater than another if its numerator is greater or its denominator is smaller.
- Less Than: A fraction is less than another if its numerator is smaller or its denominator is greater.
- Equal To: Fractions are equal if they have the same numerator and denominator, or if they are equivalent.
Real-World Applications
- Measuring: Fractions are used to measure lengths, capacities, and weights.
- Cooking: Fractions are used in recipes to specify ingredient proportions.
- Finance: Fractions are used to calculate interest rates, investments, and discounts.
Key Terms
- Proper Fraction: A fraction with a numerator smaller than the denominator.
- Improper Fraction: A fraction with a numerator equal to or greater than the denominator.
- Mixed Number: A combination of a whole number and a proper fraction.
Test your knowledge of fractions, including equivalent fractions, simplest form, operations, comparisons, and real-world applications.
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